Question: Ishaan is 2 times as old as Ashley. 21 years ago, Ishaan was 9 times as old as Ashley. How old is Ishaan now?
Answer: We can use the given information to write down two equations that describe the ages of Ishaan and Ashley. Let Ishaan's current age be $i$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $i = 2a$ 21 years ago, Ishaan was $i - 21$ years old, and Ashley was $a - 21$ years old. The information in the second sentence can be expressed in the following equation: $i - 21 = 9(a - 21)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = i / 2$ . Substituting this into our second equation, we get: $i - 21 = 9($ $(i / 2)$ $- 21)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 21 = \dfrac{9}{2} i - 189$ Solving for $i$ , we get: $\dfrac{7}{2} i = 168$ $i = \dfrac{2}{7} \cdot 168 = 48$.